It can indeed. Moisture needs be drawn from the soap, so if the air is also rather full of moisture, it might some help, such as running a dehumidifier in the room where you cure.
I cure my soap 6-8 weeks. And I live in a very humid environment. Those soaps are going into humid bathrooms, so they may as well start as they mean to go on.
I would say that the humidity may add a week or two to cure time, if you even notice any difference at all. But since you have such a humid climate, you might want to make sure you load your soaps up with a lot of shelf-stable long-lived oils to avoid DOS.
My soap is coconut oil and olive oil, with half yoghurt and water in the lye. Sf is 5% and water oil ratio 38%. Since I stopped grape seed oil have not had a lot of DOS, but lots of soda ash.